The primary objective is to compare, in a random double-blind trial, two clinical rabbit anti-thymocyte globulin (ATG) preparations: 1) A preparation of moderate immunosuppressive capability (20 days skin graft survival in Rhesus monkeys), 2) a preparation of high immunosuppressive capability (40 days Rhesus skin graft survival). Well established internal controls in the form of standardized patient management and stable patient and graft survival over a nine year period will contribute to the validity of this trial. This clinical trial represents one of the first well controlled tests of the validity of the primate skin graft assay in predicting the immunosuppressive potency of ATG as measured by effectiveness of ATG in a controlled renal transplant program. Sixty cadaveric renal transplant recipients matched for risk factors will be alternatively assigned to each two groups made up of 30 patients. Parameters monitored will include patient and graft survival, incidence and severity of acute rejection crises, incidence of infectious complications, total amount of steroids given the patient and histological and immunofluorescent studies of kidney biopsies. Monitoring the in-vivo function and the levels of thymus-derived lymphocytes, bone marrow derived lymphocytes, non-B cell cytotoxic lymphocytes and macrophages will be performed and comparison made of these cellular immune functions in patients given moderate and high potency ATG. In addition, correlations between levels and function of these immune cells and clinical parameters of graft rejection and infection will be sought. Serum factors capable of blocking the mixed lymphocyte reaction (MLC) and/or cell mediated lympholysis (CML) will be assayed in renal allograft recipient treated with high or low potency ATG. The level of blocking factors will be compared between patient groups receiving moderate and high potency ATG and attempts made to correlate these levels with the clinical parameters measured.